Confounder selection via penalized credible regions.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Accurate estimation of exposure or treatment effects requires careful selection of confounding variables.
• Including excessive covariates increases mean squared error, while omitting confounders introduces bias.

Purpose of the Study:

• To propose a novel decision-theoretic approach for confounder selection and effect estimation.
• To develop a method that balances the risks of including too many or too few confounders.

Main Methods:

• Estimating a full standard Bayesian regression model.
• Post-processing the posterior distribution using a loss function that penalizes omitted confounders.
• Leveraging existing software for efficient computation, often avoiding Markov chain Monte Carlo methods.

Main Results:

• The proposed method demonstrates computational efficiency, comparable to least squares solutions.
• Theoretical analysis confirms attractive asymptotic properties of the proposed estimator.
• Simulation studies show superior performance compared to existing confounder selection methods.

Conclusions:

• The decision-theoretic approach offers an effective strategy for confounder selection in regression analysis.
• This method provides a computationally efficient and statistically sound alternative for effect estimation.
• The approach was successfully demonstrated in estimating the impact of fine particulate matter (PM2.5) on birth weight.